Leigh Griffiths' early strike proved to be the difference between the two sides as the Hoops' final fixture of 2012 ended in disappointment.
While the champions dominated possession and created several openings, they were unable to find a way past Ben Williams, who had an inspired afternoon between the sticks for the hosts.
Celtic coach Neil Lennon made three changes to the team that defeated Dundee on Boxing Day, with Thomas Rogne, Mikael Lustig and Lassad coming into the starting XI at the expense of Charlie Mulgrew, Beram Kayal and Tony Watt.
Though Wanyama's, whose performance has been on ascendancy this season played the entire match, it was not their day as the frantic efforts they made could not help them find the target.
After a frenetic opening, it was the Hoops who had the first effort on target with Lustig firing a free-kick on target from 25 yards which Williams dealt with comfortably.
But 60 seconds later the hosts made the breakthrough. Griffiths fastened on to a long ball over the top, rounded the advancing Fraser Forster and finished expertly from an acute angle.
Celtic almost fashioned an immediate response as Georgios Samaras' deft shot hit the inside post following Lustig's cutback.
However, the offside flag was already on. The Hoops however, still remain top of the standings on 40 points six above second placed Iverness.